CN109617538A - Robust variadic sparse adaptive filter - Google Patents
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- H—ELECTRICITY
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- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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Abstract
本发明公开了一种鲁棒的变参数稀疏自适应滤波器，属于数字滤波器设计领域。该滤波器主要利用时变步长参数和控制零吸引子强度的正则化参数来加快自适应滤波器的收敛速度并降低其稳态失调。本发明公开的鲁棒的变参数稀疏自适应滤波器在输入为白色信号输入且在有脉冲噪声的影响时，其性能与传统符号滤波器相比，具有更好的收敛性能。本发明公开的鲁棒的变参数稀疏自适应滤波器可以应用于回声消除、噪声消除器、信号增强及干扰脉冲的电子、通信设备等领域。
The invention discloses a robust variable parameter sparse adaptive filter, which belongs to the field of digital filter design. The filter mainly utilizes a time-varying step size parameter and a regularization parameter that controls the strength of the zero attractor to speed up the adaptive filter's convergence speed and reduce its steady-state offset. The robust variable-parameter sparse adaptive filter disclosed by the invention has better convergence performance than the traditional symbol filter when the input is a white signal input and is influenced by impulse noise. The robust variable-parameter sparse adaptive filter disclosed by the invention can be applied to the fields of echo cancellation, noise canceller, signal enhancement and interference pulse electronics, communication equipment and the like.
Description
Technical field
The invention discloses a kind of sparse sef-adapting filters of the variable element of robust, belong to digital filter design field.
Background technique
Traditional least-mean-square filter (LMS) and normalization minimum mean-square filter (NLMS) is in sef-adapting filter
It has a wide range of applications, such as self-adaptive echo counteracting, active noise controlling and adaptation noise are eliminated.
Convergence rate, steady output rate and anti-impulse disturbances ability are three important performance indexes of sef-adapting filter.Surely
The height of state imbalance determines that sef-adapting filter approaches the precision that unknown system can reach, and the speed of convergence rate determines
Sef-adapting filter approaches the time that unknown system needs to spend, and anti-impulse disturbances ability determines the Shandong of sef-adapting filter
Stick, these three indexs affect the quality of signal processing simultaneously.
When sef-adapting filter is by impulse noise interference, the stable state of these traditional LMS and NLMS sef-adapting filters
Imbalance will increase, or even diverging.Using symbol LMS (the being denoted as SE-LMS) sef-adapting filter for taking symbolic operation to evaluated error
[Sayed A H, Adaptive filters, John Wiley&Sons, 2008], can greatly reduce impulsive noise to adaptive
Answer the influence of filter.However the SE-LMS sef-adapting filter of fixed step size, convergence rate and steady output rate cannot be simultaneously
Obtain optimal value.
In order to further decrease the steady output rate of filter, adaptively filtered using the symbol LMS (being denoted as VSSA) of variable step
Wave device [Yuan-Ping Li, Ta-Sung Lee, Bing-Fei Wu.A variable step-size sign algorithm
For channel estimation, Signal Processing, 102:304-312], which can substantially reduce filtering
The steady output rate of device.In addition, in some applications, the unknown system of sef-adapting filter estimation may be it is sparse, use SE-
LMS or VSSA sef-adapting filter is unable to fully accelerate to restrain using its sparse characteristic.
In order to further speed up the convergence rate of filter, the present invention discloses a kind of sparse adaptive filter of variable element of robust
Wave device, which, which uses, has l0The variable element notation method (being denoted as VP-SE-LMS) of norm constraint is updated.This is adaptive
Answering filter not only has stronger robustness, but also can improve the convergence rate of estimation Sparse System.It is disclosed by the invention adaptive
Filter is answered to can be used for comprising in the electronic instruments and equipment of functions such as echo cancelltion, noise elimination, channel estimation.
Summary of the invention
The sparse sef-adapting filter of the variable element of robust disclosed by the invention, using the base in absolute value error cost function
The method that a zero attractor bound term of arc tangent is added on plinth is established, and step parameter and regularization parameter are with the number of iterations
Change and adjust automatically, to improve the performance of sef-adapting filter.
The principle of technical solution of the present invention is as follows:
A kind of sparse sef-adapting filter of the variable element of robust, updates its weight vector wnSpecific step is as follows:
1) by input signal vector xnWith the weight vector w of sef-adapting filternInner product is carried out, sef-adapting filter is generated
Output yn, i.e.,Wherein: xn=[xn, xn-1..., xn-M+1]T, and xn, xn-1..., xn-M+1Indicate the n moment to n-M+
M sample value of 1 moment input signal；wn=[w0, n, w1, n..., wM-1, n]T, and w0, n, w1, n..., wM-1, nIndicate n moment weight
Vector wnM element；M is integer, and subscript T indicates transposition operation；
2) according to en=dn-ynCalculate the evaluated error e at n momentn, in which: dnIndicate the desired signal of unknown system；
3) according to ψn=median (| en|, | en-1| ..., | en-L+1|) calculate n moment to the n-L+1 moment evaluated error
{|en|, | en-1| ..., | en-L+1| intermediate value ψn, wherein median () expression asks median operation to accord with, | | it indicates to scalar
Or each element of vector carries out the operation that takes absolute value, L indicates the length of intermediate value window；
4) basisWithTo calculate the estimation of additional mean square error
Value, whereinIndicate evaluated errorIn the smooth value at n moment, β is smoothing factor,For additional mean square error ζnEstimated value,For the minimum value of additional mean square error,For noise znVariance；
5) basis WithCalculate time change step length parameter
The intermediate variable a needed with time-varying regularization parametern、bn、cn、p1n、gnAnd p2n, in which: sgn { } is indicated to scalar or vector
Each element carries out taking symbolic operation,Indicate that the element of former and later two vector corresponding positions of the operator is divided by respectively,It is defeated
Enter signal xnVariance；
6) basisCalculate the time change step length parameter of estimationAccording toCalculate the time-varying regularization parameter of estimation
7) by the time change step length parameter of estimationWith the time-varying regularization parameter of estimationIt is limited to nonnegative value, even
8) basisCalculate smoothed out time-varying step
Long parameter μnWith smoothed out time-varying regularization parameter ρn, whereinFor smoothing factor, μmaxFor the step parameter maximum value of permission；
9) basisCalculate the n+1 moment
The outer mean square error of jot
10) formula is usedUpdate weight vector wn。
Beneficial effect
Scheme in compared with the existing technology, the sparse sef-adapting filter of the variable element of robust disclosed by the invention maintain
It is estimated preferably constringency performance when Sparse System and inhibits the interference of impulsive noise.
Detailed description of the invention
The invention will be further described with reference to the accompanying drawings and embodiments:
Fig. 1 is the sparse sef-adapting filter block diagram of variable element of robust；
Under the conditions of Fig. 2 is described in the embodiment, the normalization mean-squared departure of SE-LMS, VSSA and VP-SE-LMS filter
Learning curve compares figure.
Specific embodiment
Embodiment
The present embodiment compares SE-LMS, VSSA sef-adapting filter by the method for computer-experiment and the present invention discloses
VP-SE-LMS sef-adapting filter convergence rate and steady output rate.
One, experiment condition:
Experimental setup is as shown in Figure 1, input signal xnFor the white Gaussian noise of zero-mean, variance isMeasurement is made an uproar
Sound is by white Gaussian noise znWith impulsive noise θnSynthesis, wherein znVariance beImpulsive noise θnBy Bernoulli process
τnWith Gaussian process tnProduct generate, i.e. θn=tnτn, and probability distribution meets P (τn=1)=0.01, P (τn=0)=
0.99.In MATLAB environment, the weight vector w of unknown system is generatedo=[0.8,0.5,0.3,0.2,0.1,0.05, zeros
(1,36), -0.05, -0.1, -0.2, -0.3, -0.5, -0.8]T。
Two, experimental procedures:
1. initialization:
w1=[zeros (Isosorbide-5-Nitrae 8)]T, ρ0=0, μ0=0.01, L=11,β=
0.997；
2. updating weight vector w by following each expression formula at the moment of n >=1n:
1)
2)en=dn-yn；
3)ψn=median (| en|, | en-1| ..., | en-L+1|)；
4)
5)
6)
7)
8)
9)
10)
Three, experimental results:
Performance indicator, expression formula 20log are used as using the normalization mean-squared departure (NMSD) changed with the number of iterations10
(||wo-wn||/||wo| |), unit is decibel (dB).All NMSD curves are the result that 100 independent experiments are averaged.Such as
Shown in Fig. 2, the weight vector of unknown system is estimated, VP-SE-LMS sef-adapting filter ratio SE- disclosed by the invention
LMS sef-adapting filter has lower steady output rate, has faster convergence rate than VSSA sef-adapting filter.
The above embodiments merely illustrate the technical concept and features of the present invention, and its object is to allow person skilled in the art
It cans understand the content of the present invention and implement it accordingly, it is not intended to limit the scope of the present invention.It is all smart according to the present invention
The equivalent transformation or modification that refreshing essence is done, should be covered by the protection scope of the present invention.
Claims (3)
1. a kind of sparse sef-adapting filter of the variable element of robust, it is characterised in that: the sef-adapting filter uses variable step
Parameter updates sef-adapting filter weight vector with the change regularization parameter for controlling zero attractor intensity.
2. the sparse sef-adapting filter of the variable element of robust according to claim 1, it is characterised in that: the adaptive filter
Wave device estimates the step-size parameter mu at n moment using following stepsnWith regularization parameter ρn
1) by input signal vector xnWith the weight vector w of sef-adapting filternInner product is carried out, the defeated of sef-adapting filter is generated
Y outn, i.e.,Wherein: xn=[xn, xn-1..., xn-M+1]T, and xn, xn-1..., xn-M+1When indicating that the n moment is to n-M+1
Carve M sample value of input signal；wn=[w0, n, w1, n..., wM-1, n]T, and w0, n, w1, n..., wM-1, nIndicate n moment weight vector
wnM element；M is integer, and subscript T indicates transposition operation；
2) according to en=dn-ynCalculate the evaluated error e at n momentn, wherein dnIndicate the desired signal of unknown system；
3) according to ψn=median (| en|, | en-1| ..., | en-L+1|) calculate n moment to the n-L+1 moment evaluated error | en|,
|en-1| ..., | en-L+1| intermediate value ψn, wherein median () expression asks median operation to accord with, | | it indicates to scalar or vector
Each element carry out the operation that takes absolute value, L indicates the length of intermediate value window；
4) basisWithCalculate the estimated value of additional mean square error,
InIndicate evaluated errorIn the smooth value at n moment, β is smoothing factor,For additional mean square error ζnEstimated value,
For the minimum value of additional mean square error,For without impulsive noise znVariance；
5) basis WithCalculate time change step length parameter
The intermediate variable a needed with time-varying regularization parametern、bn、cn、p1n、gnAnd p2n, in which: sgn { } is indicated to scalar or vector
Each element carries out taking symbolic operation,Indicate that the element of former and later two vector corresponding positions of the operator is divided by respectively,It is defeated
Enter signal xnVariance；
6) basisCalculate the time change step length parameter of estimationAnd according toCalculate the time-varying regularization parameter of estimation
7) by the time change step length parameter of estimationWith the time-varying regularization parameter of estimationIt is limited to nonnegative value, even
8) basisCalculate smoothed out time change step length ginseng
Number μnWith smoothed out time-varying regularization parameter ρn, whereinFor smoothing factor, μmaxFor the step parameter maximum value of permission；
9) basisCalculate the n+1 moment most
Small additional mean square error
3. the sparse sef-adapting filter of the variable element of robust according to claim 2, it is characterised in that: the adaptive filter
Wave device uses calculating formulaUpdate weight vector wn。
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| CN111181531A (en) * | 2020-01-22 | 2020-05-19 | 苏州大学 | Regularization deviation compensation symbol subband self-adaptive filter |
| CN111277244A (en) * | 2020-02-06 | 2020-06-12 | 苏州大学 | Variable-step zero-attraction normalization double-symbol adaptive filter |
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| CN111181531B (en) * | 2020-01-22 | 2023-05-19 | 苏州大学 | Variable regularization deviation compensation symbol sub-band adaptive filter |
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| CN111884625A (en) * | 2020-07-28 | 2020-11-03 | 苏州大学 | A Variable Step Sparse Augmented Complex Adaptive Filter |
| CN111884625B (en) * | 2020-07-28 | 2024-03-01 | 苏州大学 | Variable step-length sparse augmentation complex number self-adaptive filter |
| CN112886947A (en) * | 2021-01-26 | 2021-06-01 | 苏州大学 | Variable-step robust affine projection adaptive filter |
| CN112886947B (en) * | 2021-01-26 | 2024-03-22 | 苏州大学 | Variable step length robust affine projection self-adaptive filter |
| CN113409806B (en) * | 2021-01-28 | 2023-12-22 | 合肥工业大学 | Zero-attraction echo cancellation method based on arctangent function |
| CN113409806A (en) * | 2021-01-28 | 2021-09-17 | 合肥工业大学 | Zero attraction echo cancellation method based on arc tangent function |
| CN113225045B (en) * | 2021-03-25 | 2023-06-23 | 苏州大学 | Sparse-boosted affine projection adaptive filters with low computational complexity |
| CN113225045A (en) * | 2021-03-25 | 2021-08-06 | 苏州大学 | Low-computation-complexity sparsely-promoted affine projection adaptive filter |
| CN114172490A (en) * | 2021-12-08 | 2022-03-11 | 哈尔滨工程大学 | A Robust Adaptive Noise Removal Method Based on Ekblom Norm |
| CN114172490B (en) * | 2021-12-08 | 2024-07-02 | 哈尔滨工程大学 | Ekblom norm-based robust self-adaptive noise elimination method |
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